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A batch arrival Bernoulli vacation queue with a random setup time under restricted admissibility policy

Author

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  • Gautam Choudhury
  • Kailash C. Madan

Abstract

We consider a batch arrival queue with a Bernoulli vacation bschedule, where, after completion of a service, the server either goes for a vacation of random length with probability θ(0 ≤ θ ≤ 1) or may continue to serve the next unit, if any, with probability (1−θ), under a Restricted Admissibility (RA) policy of arriving batches with a random Setup Time (SET). Unlike the usual batch arrival queueing system, the RA-policy differs during a busy period and a vacation period and hence all arriving batches are not allowed to join the system at all times. We derive the steady state queue size distributions at a random point of time as well as at a departure epoch. Also, we obtain some important performance measures of this model. Further, we demonstrate the existence of stochastic decomposition result for this type of model.

Suggested Citation

  • Gautam Choudhury & Kailash C. Madan, 2007. "A batch arrival Bernoulli vacation queue with a random setup time under restricted admissibility policy," International Journal of Operational Research, Inderscience Enterprises Ltd, vol. 2(1), pages 81-97.
  • Handle: RePEc:ids:ijores:v:2:y:2007:i:1:p:81-97
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    Cited by:

    1. K. Sikdar & S. K. Samanta, 2016. "Analysis of a finite buffer variable batch service queue with batch Markovian arrival process and server’s vacation," OPSEARCH, Springer;Operational Research Society of India, vol. 53(3), pages 553-583, September.

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